Problem: Solve for $x$ and $y$ using elimination. ${3x-3y = -21}$ ${4x-2y = -10}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $3$ ${-12x+12y = 84}$ $12x-6y = -30$ Add the top and bottom equations together. $6y = 54$ $\dfrac{6y}{{6}} = \dfrac{54}{{6}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {3x-3y = -21}\thinspace$ to find $x$ ${3x - 3}{(9)}{= -21}$ $3x-27 = -21$ $3x-27{+27} = -21{+27}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {4x-2y = -10}\thinspace$ and get the same answer for $x$ : ${4x - 2}{(9)}{= -10}$ ${x = 2}$